Problem: If $x \diamond y = x^{2}-2y^{2}$ and $x \oplus y = 7x+y$, find $(-1 \diamond 1) \oplus 5$.
First, find $-1 \diamond 1$ $ -1 \diamond 1 = (-1)^{2}-2(1^{2})$ $ \hphantom{-1 \diamond 1} = -1$ Now, find $-1 \oplus 5$ $ -1 \oplus 5 = (7)(-1)+5$ $ \hphantom{-1 \oplus 5} = -2$.